OPTIMAL TIME MOMENTS IN A UNIFORM 1-BULLET SILENT DUEL WITH SCALED EXPONENTIALLY-CONVEX ACCURACY

Abstract

The finite 1-bullet silent duel is considered, involving two duelists who shoot with exponentially-convex accuracy through a uniformly quantized time. The duel is a symmetric matrix game whose optimal value is 0, and each of the duelists has the same optimal behavior, whether it is in pure or mixed strategies. The actual beginning is never optimal in the duel. Apart from the very end of the duel, the conditions for the optimal time moment existence are found. Numerical experiments confirm that the optimality can be manipulated by changing the accuracy factor that scales the payoffs. The results are applicable in systems under limited or censored communication with uncertainty, latency, and lucrative delayed actions. Some examples of such set-ups are time-sensitive information release (privacy and censorship), queueing and load balancing (information science and telecommunication systems), and block proposal timing for decentralized consensus protocols (in Proof-of-Work and Proof-of-Stake).